






"""simple docstring"""
from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import rescale, resize, to_channel_dimension_format
from ...image_utils import (
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
 import PIL


snake_case : Optional[int]     		=		logging.get_logger(__name__)


def 							A						(				__snake_case: Optional[Any] ,     __snake_case: Tuple  )    ->		Union[str, Any]:

       """simple docstring"""





       __magic_name__      				=    b.T
       __magic_name__      				=    np.sum(np.square(__snake_case  ) ,     axis=1  )
       __magic_name__      				=    np.sum(np.square(__snake_case  ) ,     axis=0  )
       __magic_name__      				=    np.matmul(__snake_case ,     __snake_case  )
       __magic_name__      				=    aa[:, None] - 2 * ab + ba[None, :]
       return d


def 							A						(				__snake_case: int ,     __snake_case: str  )    ->		Tuple:

       """simple docstring"""





       __magic_name__      				=    x.reshape(-1 ,     3  )
       __magic_name__      				=    squared_euclidean_distance(__snake_case ,     __snake_case  )
       return np.argmin(__snake_case ,     axis=1  )






class        UpperCamelCase__ (				a_):







    """simple docstring"""
    __UpperCAmelCase           = ["""pixel_values"""]







    def __init__(		self :	List[str]				,    UpperCamelCase_ :	Optional[Union[List[List[int]], np.ndarray]] = None				,    UpperCamelCase_ :	bool = True				,    UpperCamelCase_ :	Dict[str, int] = None				,    UpperCamelCase_ :	PILImageResampling = PILImageResampling.BILINEAR				,    UpperCamelCase_ :	bool = True				,    UpperCamelCase_ :	bool = True				,    **UpperCamelCase_ :	int				,    ):





           '''simple docstring'''

           super().__init__(**UpperCamelCase_ )
           __magic_name__      				=    size if size is not None else {'height': 2_5_6, 'width': 2_5_6}
           __magic_name__      				=    get_size_dict(UpperCamelCase_ )
           __magic_name__      				=    np.array(UpperCamelCase_ ) if clusters is not None else None
           __magic_name__      				=    do_resize
           __magic_name__      				=    size
           __magic_name__      				=    resample
           __magic_name__      				=    do_normalize
           __magic_name__      				=    do_color_quantize







    def 				a__			(		self :	str				,    UpperCamelCase_ :	np.ndarray				,    UpperCamelCase_ :	Dict[str, int]				,    UpperCamelCase_ :	PILImageResampling = PILImageResampling.BILINEAR				,    UpperCamelCase_ :	Optional[Union[str, ChannelDimension]] = None				,    **UpperCamelCase_ :	Tuple				,    ):





           '''simple docstring'''

           __magic_name__      				=    get_size_dict(UpperCamelCase_ )
           if "height" not in size or "width" not in size:
                  raise ValueError(f"""Size dictionary must contain both height and width keys. Got {size.keys()}""" )
           return resize(
               UpperCamelCase_				,    size=(size['height'], size['width'])				,    resample=UpperCamelCase_				,    data_format=UpperCamelCase_				,    **UpperCamelCase_ )







    def 				a__			(		self :	Any				,    UpperCamelCase_ :	np.ndarray				,    UpperCamelCase_ :	Optional[Union[str, ChannelDimension]] = None				,    ):





           '''simple docstring'''

           __magic_name__      				=    rescale(image=UpperCamelCase_				,    scale=1 / 127.5				,    data_format=UpperCamelCase_ )
           __magic_name__      				=    image - 1
           return image







    def 				a__			(		self :	int				,    UpperCamelCase_ :	ImageInput				,    UpperCamelCase_ :	bool = None				,    UpperCamelCase_ :	Dict[str, int] = None				,    UpperCamelCase_ :	PILImageResampling = None				,    UpperCamelCase_ :	bool = None				,    UpperCamelCase_ :	Optional[bool] = None				,    UpperCamelCase_ :	Optional[Union[List[List[int]], np.ndarray]] = None				,    UpperCamelCase_ :	Optional[Union[str, TensorType]] = None				,    UpperCamelCase_ :	Optional[Union[str, ChannelDimension]] = ChannelDimension.FIRST				,    **UpperCamelCase_ :	Optional[int]				,    ):





           '''simple docstring'''

           __magic_name__      				=    do_resize if do_resize is not None else self.do_resize
           __magic_name__      				=    size if size is not None else self.size
           __magic_name__      				=    get_size_dict(UpperCamelCase_ )
           __magic_name__      				=    resample if resample is not None else self.resample
           __magic_name__      				=    do_normalize if do_normalize is not None else self.do_normalize
           __magic_name__      				=    do_color_quantize if do_color_quantize is not None else self.do_color_quantize
           __magic_name__      				=    clusters if clusters is not None else self.clusters
           __magic_name__      				=    np.array(UpperCamelCase_ )

           __magic_name__      				=    make_list_of_images(UpperCamelCase_ )

           if not valid_images(UpperCamelCase_ ):
                  raise ValueError(
                      'Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '
                      'torch.Tensor, tf.Tensor or jax.ndarray.' )

           if do_resize and size is None or resample is None:
                  raise ValueError('Size and resample must be specified if do_resize is True.' )

           if do_color_quantize and clusters is None:
                  raise ValueError('Clusters must be specified if do_color_quantize is True.' )

           # All transformations expect numpy arrays.
           __magic_name__      				=    [to_numpy_array(UpperCamelCase_ ) for image in images]

           if do_resize:
                  __magic_name__      				=    [self.resize(image=UpperCamelCase_				,    size=UpperCamelCase_				,    resample=UpperCamelCase_ ) for image in images]

           if do_normalize:
                  __magic_name__      				=    [self.normalize(image=UpperCamelCase_ ) for image in images]

           if do_color_quantize:
                  __magic_name__      				=    [to_channel_dimension_format(UpperCamelCase_				,    ChannelDimension.LAST ) for image in images]
                  # color quantize from (batch_size, height, width, 3) to (batch_size, height, width)
                  __magic_name__      				=    np.array(UpperCamelCase_ )
                  __magic_name__      				=    color_quantize(UpperCamelCase_				,    UpperCamelCase_ ).reshape(images.shape[:-1] )

                  # flatten to (batch_size, height*width)
                  __magic_name__      				=    images.shape[0]
                  __magic_name__      				=    images.reshape(UpperCamelCase_				,    -1 )

                  # We need to convert back to a list of images to keep consistent behaviour across processors.
                  __magic_name__      				=    list(UpperCamelCase_ )
           else:
                  __magic_name__      				=    [to_channel_dimension_format(UpperCamelCase_				,    UpperCamelCase_ ) for image in images]

           __magic_name__      				=    {'input_ids': images}
           return BatchFeature(data=UpperCamelCase_				,    tensor_type=UpperCamelCase_ )







"""simple docstring"""
def 							A						(				__snake_case: int = 1_0_0_0_0_0_0  )    ->		int:

       """simple docstring"""





       __magic_name__      				=    limit + 1
       __magic_name__      				=    [0] * limit
       for first_term in range(1 ,     __snake_case  ):
              for n in range(__snake_case ,     __snake_case ,     __snake_case  ):
                     __magic_name__      				=    first_term + n / first_term
                     if common_difference % 4:  # d must be divisble by 4
                            continue
                     else:
                            common_difference /= 4
                            if (
                                first_term > common_difference
                                and first_term < 4 * common_difference
                            ):  # since x,y,z are positive integers
                                   frequency[n] += 1  # so z>0 and a>d ,also 4d<a

       __magic_name__      				=    sum(1 for x in frequency[1:limit] if x == 1_0  )

       return count


if __name__ == "__main__":
 print(f"""{solution() = }""")